Every unitary operator U : X → X is normal. b) A matrix is unitary if and only if it is invertible. c) If two matrices are unitarily equivalent, then they are also similar. d) The sum of self-adjoint operators is self-adjoint. e) The adjoint of a unitary operator is unitary. f) The adjoint of a normal operator is normal. g) If all eigenvalues of a linear operator are 1, then the operator must be unitary or orthogonal. h) If all eigenvalues of a normal operator are 1, then the operator is identity. i) A linear operator may preserve norm but not the inner product.

Arecent study focused on the number of times men and women who live alone buy take-out dinner in a month. assume that the distributions follow the normal probability distribution and the population standard deviations are equal. the information is summarized below. statistic men women sample mean 24.85 21.33 sample standard deviation 5.54 4.93 sample size 34 36 at the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? state the decision rule for 0.01 significance level: h0: μmen= μwomen h1: μmen ≠ μwomen. (negative amounts should be indicated by a minus sign. round your answers to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? what is the p-value? (round your answer to 3 decimal places.)